Since you reply diredctly and I see missunderstanding, I have to post:

Of course it is possible to make a rough estimate and hope that it is valid in at least some circumstances, thats not only possible, it is fairly simple and already has been done. It is impossible to do without "hardcoded fiddle factors" though, which was my point. (And if you streamline item modifiers so much that looking at the scalar value of an item is enough to decide if its an upgrade, you ruined the game.)

Again, what are you trying to achieve ? "Better balance" is about as meaningful as "more fun".

I guess we'll let the people who are actually touching the code decide on matters of impossibility.

The goal, as I understand it, is primarily to have something we can objectively measure that can then be used as a tool to guide balance decisions. Of course final balance decisions should not be made solely on the basis of these tools; what matters is that the game is fun to play. But it can be very helpful to be able to ask "fizzix says he had this game where he found tons of overpowered stuff, was that just a lucky game or is that actually representative of the current state of things?" Not to mention, if we decide to do something like "make powerful items more rare", say -- item distribution is super complicated with a myriad interdependent factors. Tools that can gather stats and objectively measure item power can tell us if we actually did what we set out to do.

tl;dr making decisions in the absence of good data is super hard and leads to a lot of trial and error, so let's get some good data.

Slays and Brands - here there is a big sum done across all monsters of (monster power) * (best multiplier). This is appealing to me as a mathematician, except for the fact that it forms a small part of the total object power, and so is a tiny little piece of precision in a sea of fudge factors. Better just to treat slays and brands like object flags - they get a fixed value, maybe some bonuses for multiples, and be done with it.

So I have looked into this a little further, and have some very interesting (to me, anyway) results.

First, the basic calculation of slay/brand powers works like this:

Start with a combination of brands and slays from a weapon

For each monster, calculates the best multiplier to the damage dice from those slays/brands, and multiplies it by monster power

Adds that all up, and divides it by total monster power

So, if you believe the monster power values, this should give an average multiplier for that slay/brand combination. Even if you don't, you would expect it to be close to that. A table of some of these multipliers (approximately):

Zarcuthra, which has fire brand and slay everything (including *slay* dragon) gets a multiplier of 2.2.

The power code then goes on to add (this multiple * dice power) to the overall power (so effectively weapons with a slay/brand, no matter how weak, get their dice counted twice), and then goes further to give bonuses for multiple slays, *slay*s and brands.

Conclusions:

Slay evil is easily the best slay/brand (as most people kind of suspected); brands are also handy, with acid slightly better than the others.

All the other slays, however useful situationally, are on average unimportant.

This is moderated a bit by the fact that slays tend to get better deeper in the dungeon (many high-value targets are demons, dragons and undead), whereas brands tend to get worse (more monsters resist).

The power code massively overvalues all slays and brands; with the exception of slay evil, they should have almost no effect on power (compared to, say, +to-dam).

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One Ring to rule them all, One Ring to find them,
One Ring to bring them all and in the darkness bind them.

You are undervaluing *slay* dragon because they are so common and such high-value kills. Since you can select monsters to kill (except for bosses) this calculation can never be really accurate. And slay animal is worse, because nearly all animals can be killed with lightning or acid brand.

There's a fallacy in the calculation. If I have a weapon that does a lot of damage versus dragons and not much versus everything else, I'm going to actively seek out dragons to kill, and consciously avoid the other monsters. In the infinite inventory case, I would keep a strong weapon against dragons, demons, undead etc. Obviously, in the finite inventory case this isn't possible, so a weapon with just slay dragon and nothing else is pretty useless.

This is a lot more clear with ammo, where with the quiver, the inventory pressure is a lot less for keeping multiple branded ammo. Often the decision of whether or not to kill Ancalagon depends mainly on whether I have powerful ammo of slay dragon.

There's a fallacy in the calculation. If I have a weapon that does a lot of damage versus dragons and not much versus everything else, I'm going to actively seek out dragons to kill, and consciously avoid the other monsters. In the infinite inventory case, I would keep a strong weapon against dragons, demons, undead etc. Obviously, in the finite inventory case this isn't possible, so a weapon with just slay dragon and nothing else is pretty useless.

Well, yes. There is an assumption in there that you go through and kill one of every monster exactly once, which is clearly not true. It's remarkably easy to lie with statistics

One thing I didn't really mention was that on weapons with multiple slays and brands, the average multiplier was very close to being just the average multiplier for the best slay/brand. So slay evil and slay dragon is almost the same as slay evil; as you point out, though, that combination would encourage the player to fight evil things, and especially dragons.

So I probably went a bit far in my conclusions, but the whole process has helped my thinking on changes to the power calculation. This forum is actually quite useful

__________________
One Ring to rule them all, One Ring to find them,
One Ring to bring them all and in the darkness bind them.

You are undervaluing *slay* dragon because they are so common and such high-value kills. Since you can select monsters to kill (except for bosses) this calculation can never be really accurate. And slay animal is worse, because nearly all animals can be killed with lightning or acid brand.

They used to be high value, but not anymore. Younger dragons (d) still are, but the big ones (D) have had their loot downgraded somewhere in one of the changes. I have been watching for a while now, and in dozens of games I got exactly 1 artifact from a "D" (non-unique).

Item valuation is ridiculously complex. It matters how rare the resistance is, how powerful the equipment slot is, how strong MAX breath damage is, and MAX spell damage as well (for darkness in particular.) And how common the attack is.

+1

We have a choice: imperfect algorithmic power, or imperfect simplified power. The same goes for monsters. I don't see the logic of simplifying one but not the other. If you're hand-crafting monster power, you can hand-craft item prices and randarts! (Take a look at Greg Wooledge's original randart code to see what I mean.)

If you want to make randarts less random and more balanced, take a look at the themes code in v4.

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"3.4 is much better than 3.1, 3.2 or 3.3. It still is easier than 3.0.9, but it is more convenient to play without being ridiculously easy, so it is my new favorite of the versions." - Timo Pietila